The invention relates to an apparatus for transporting workpeices. The apparatus includes a transport path (track) system for transport wagons (carriages). The transport path system which passes by workplaces, is composed of route modules and point (switching) modules, each provided with running surfaces for the transport wagons and support surfaces for the lateral guidance of the wagons. In the point modules the lateral guidance is effected by guide elements, such as rotatably mounted rollers which are arranged on the opposite transport wagon sides that are oriented parallel to the plane of the transport path. The guide elements are perpendicular to the plane of the running surfaces and engage in guides of the point modules. The engagement on a side of the transport wagon parallel to the transport path is discontinued by changing the setting of the guide elements at the point module and/or on the transport wagons from an operative position determining the direction of travel to an inoperative, lateral position. In a known apparatus of this generic type, the transport path system is provided with simple point modules, on which only the transport wagons arriving on one of the two coaxially opposite point branches can optionally be transferred into the coaxially opposite point branch or into the point branch which is diverted at a right an design requires additional point connections to make it possible for the travel paths of the transport wagons to be fixed in an as flexible and optimum manner as possible in a network transport path system.